NavList:

I tried to guess where you are. I started by assuming the US.

The LHA computation of the difference in day length that rounds to whole 35s places you between 42°33' and 43°16' on US west coast and 42°14' and 42°56' US East coast. The only major settlements in this band are in the East (Albany, Detroit, and Boston), so I'll assume East coast. Conveniently, all of them use UTC-4.

The time that the Moon spends above the horizon places you between 41°21' N and 41°35' N, and its Greenwich offset puts you 13.5 degrees west from the timezone (UTC-4) centre, i.e. 73.5° W. Disappointingly, the latitude estimates do not overlap.

Perhaps the Nautical Almanac uses a different definition of moonrise/moonset than your weather website, which would significantly affect the latitude estimate. In that case I'd be inclined to trust the Sun-based calculation of latitude since taking the difference between days cancels out any discrepancy caused by the definition of sunset/sunrise. For longitude, I'd expect the Moon data to cancel out, so my final guess would be Albany, NY, give or take 30nm.

Now, how far off did I end up? :)